Estimation of the smaller and larger of two exponential location parameters

Abstract

Assume independent random samples are drawn from two populations which are exponentially distributed with unknown location parameters and a common known scale parameter. We want to estimate the maximum and the minimum of the unknowo location paremeters. In this paper several estimators are proposed which are better than the natural estimations in terms of absolute bias and /or meaqn squared error.

Keywords:

• Maximum likelihood estimator
• absolute bias
• mean squared error
• best affine equivariant estimator

AMS 1980 Subject Classification:

• Primary:62C15
• Secondary:62F10